arXiv:1009.2731v2 [hep-ex] 7 Oct 2010
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2010-029 14 September 2010
Measurement of σ pp → bbX
at
√
s = 7 TeV in the forward region
The LHCb Collaboration 1
Abstract
Decays of b hadrons into final states containing a D0 meson and a muon are used to
measure the bb production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. In the pseudorapidity interval 2 < η < 6 and integrated over all transverse momenta we find that the average cross-section to produce b-flavoured or b-flavoured hadrons is (75.3±5.4±13.0) µb.
Keywords: LHC, b-hadron, cross-section, bottom production PACS: 14.65.Fy, 13.10.He, 13.75Cs, 13.85-t
1
The LHCb Collaboration
R. Aaij23, C. Abellan Beteta35,m, B. Adeva36, M. Adinolfi42, C. Adrover6, A. Affolder48,
M. Agari10, Z. Ajaltouni5, J. Albrecht37, F. Alessio6,37, M. Alexander47, M. Alfonsi18,
P. Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J. Amoraal23, J. Anderson39,
R. Antunes Nobrega22,k, R. Appleby50, O. Aquines Gutierrez10, A. Arefyev30, L. Arrabito53,
M. Artuso52, E. Aslanides6, G. Auriemma22,l, S. Bachmann11, Y. Bagaturia11, D.S. Bailey50, V. Balagura30,37, W. Baldini16, G. Barber49, C. Barham43, R.J. Barlow50, S. Barsuk7, S. Basiladze31, A. Bates47, C. Bauer10, Th. Bauer23, A. Bay38, I. Bediaga1, T. Bellunato20,i, K. Belous34, I. Belyaev23,30, M. Benayoun8, G. Bencivenni18, R. Bernet39, R.P. Bernhard39, M.-O. Bettler17,37, M. van Beuzekom23, J.H. Bibby51, S. Bifani12, A. Bizzeti17,g,
P.M. Bjørnstad50, T. Blake49, F. Blanc38, C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V. Bocci22, B. Bochin29, E. Bonaccorsi37, A. Bondar33, N. Bondar29,37, W. Bonivento15, S. Borghi47, A. Borgia52, E. Bos23, T.J.V. Bowcock48, C. Bozzi16, T. Brambach9,
J. van den Brand24, L. Brarda37, J. Bressieux38, S. Brisbane51, M. Britsch10, N.H. Brook42,
H. Brown48, S. Brusa16, A. B¨uchler-Germann39, A. Bursche39, J. Buytaert37, S. Cadeddu15,
J.M. Caicedo Carvajal37, O. Callot7, M. Calvi20,i, M. Calvo Gomez35,m, A. Camboni35,
W. Cameron49, L. Camilleri37, P. Campana18, A. Carbone14, G. Carboni21,j, R. Cardinale19,h,
A. Cardini15, J. Carroll48, L. Carson36, K. Carvalho Akiba23, G. Casse48, M. Cattaneo37,
B. Chadaj37, M. Charles51, Ph. Charpentier37, J. Cheng3, N. Chiapolini39, A. Chlopik27,
J. Christiansen37, P. Ciambrone18, X. Cid Vidal36, P.J. Clark46, P.E.L. Clarke46,
M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V. Coco52, J. Cogan6, P. Collins37, A. Comerma-Montells35, F. Constantin28, G. Conti38, A. Contu51, P. Cooke48, M. Coombes42, B. Corajod37, G. Corti37, G.A. Cowan46, R. Currie46, B. D’Almagne7, C. D’Ambrosio37, I. D’Antone14, W. Da Silva8, E. Dane’18, P. David8, I. De Bonis4, S. De Capua21,j,
M. De Cian39, F. De Lorenzi12, J.M. De Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, G. Decreuse37, H. Degaudenzi38,37, M. Deissenroth11, L. Del Buono8, C.J. Densham45,
C. Deplano15, O. Deschamps5, F. Dettori15,c, J. Dickens43, H. Dijkstra37, M. Dima28, S. Donleavy48, P. Dornan49, D. Dossett44, A. Dovbnya40, R. Dumps37, F. Dupertuis38, L. Dwyer48, R. Dzhelyadin34, C. Eames49, S. Easo45, U. Egede49, V. Egorychev30,
S. Eidelman33, D. van Eijk23, F. Eisele11, S. Eisenhardt46, L. Eklund47, D.G. d’Enterria35,n,
D. Esperante Pereira36, L. Est`eve43, E. Fanchini20,i, C. F¨arber11, G. Fardell46, C. Farinelli23,
S. Farry12, V. Fave38, G. Felici18, V. Fernandez Albor36, M. Ferro-Luzzi37, S. Filippov32,
C. Fitzpatrick46, W. Flegel37, F. Fontanelli19,h, C. Forti18, R. Forty37, C. Fournier37,
B. Franek45, M. Frank37, C. Frei37, M. Frosini17,e, J.L. Fungueirino Pazos36, S. Furcas20,
A. Gallas Torreira36, D. Galli14,b, M. Gandelman2, P. Gandini51, Y. Gao3, J-C. Garnier37,
L. Garrido35, D. Gascon35, C. Gaspar37, A. Gaspar De Valenzuela Cue35,m, J. Gassner39, N. Gauvin38, P. Gavillet37, M. Gersabeck37, T. Gershon44, Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C. G¨obel54, D. Golubkov30, A. Golutvin49,30,37, A. Gomes1, G. Gong3, H. Gong3, H. Gordon51, M. Grabalosa G´andara35, V. Gracco19,h, R. Graciani Diaz35,
L.A. Granado Cardoso37, E. Graug´es35, G. Graziani17, A. Grecu28, S. Gregson43, G. Guerrer1, B. Gui52, E. Gushchin32, Yu. Guz34,37, Z. Guzik27, T. Gys37, G. Haefeli38, S.C. Haines43, T. Hampson42, S. Hansmann-Menzemer11, R. Harji49, N. Harnew51, P.F. Harrison44, J. He7, K. Hennessy48, P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, A. Hicheur38, E. Hicks48, H.J. Hilke37, W. Hofmann10, K. Holubyev11, P. Hopchev4, W. Hulsbergen23,
P. Hunt51, T. Huse48, R.S. Huston12, D. Hutchcroft48, F. Iacoangeli22, V. Iakovenko7,41,
C. Iglesias Escudero36, C. Ilgner9, P. Ilten12, J. Imong42, R. Jacobsson37, M. Jahjah Hussein5,
O. Jamet37, E. Jans23, F. Jansen23, P. Jaton38, B. Jean-Marie7, M. John51, D. Johnson51,
C.R. Jones43, B. Jost37, F. Kapusta8, T.M. Karbach9, A. Kashchuk29, S. Katvars43,
J. Keaveney12, U. Kerzel43, T. Ketel24, A. Keune38, S. Khalil52, B. Khanji6, Y.M. Kim46,
M. Knecht38, S. Koblitz37, A. Konoplyannikov30, P. Koppenburg23, M. Korolev31,
K. Kruzelecki37, M. Kucharczyk25, I. Kudryashov31, S. Kukulak25, R. Kumar14,37,
T. Kvaratskheliya30, V.N. La Thi38, D. Lacarrere37, G. Lafferty50, A. Lai15, R.W. Lambert37, G. Lanfranchi18, C. Langenbruch11, T. Latham44, R. Le Gac6, J.-P. Lees4, R. Lef`evre5,
A. Leflat31,37, J. Lefran¸cois7, F. Lehner39, M. Lenzi17, O. Leroy6, T. Lesiak25, L. Li3, Y.Y. Li43, L. Li Gioi5, J. Libby51, M. Lieng9, R. Lindner37, S. Lindsay48, C. Linn11, B. Liu3, G. Liu37, S. L¨ochner10, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-March38, P. Loveridge45, J. Luisier38, B. M’charek24, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc10, O. Maev29, J. Magnin1, A. Maier37, S. Malde51, R.M.D. Mamunur37, G. Manca15,c,37, G. Mancinelli6, N. Mangiafave43, U. Marconi14, R. M¨arki38, J. Marks11, G. Martellotti22, A. Martens7, L. Martin51,
D. Martinez Santos36, A. Massafferri1, Z. Mathe12, C. Matteuzzi20, V. Matveev34, E. Maurice6,
B. Maynard52, A. Mazurov32, G. McGregor50, R. McNulty12, C. Mclean14, M. Merk23,
J. Merkel9, M. Merkin31, R. Messi21,j, S. Miglioranzi37, M.-N. Minard4, G. Moine37,
S. Monteil5, D. Moran12, J. Morant37, P. Morawski25, J.V. Morris45, J. Moscicki37,
R. Mountain52, I. Mous23, F. Muheim46, K. M¨uller39, R. Muresan38, F. Murtas18, B. Muryn26,
M. Musy35, J. Mylroie-Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, J. Nardulli45, A. Nawrot27, M. Nedos9, M. Needham38, N. Neufeld37, P. Neustroev29, M. Nicol7, L. Nicolas38, S. Nies9, V. Niess5, N. Nikitin31, A. Noor48, A. Oblakowska-Mucha26, V. Obraztsov34,
S. Oggero23, O. Okhrimenko41, R. Oldeman15,c, M. Orlandea28, A. Ostankov34, B. Pal52, J. Palacios39, M. Palutan18, J. Panman37, A. Papadelis23, A. Papanestis45, M. Pappagallo13,a, C. Parkes47,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49, S.K. Paterson49,37, G.N. Patrick45, C. Patrignani19,h, E. Pauna28, C. Pauna (Chiojdeanu)28,
C. Pavel (Nicorescu)28, A. Pazos Alvarez36, A. Pellegrino23, G. Penso22,k, M. Pepe Altarelli37,
S. Perazzini14,b, D.L. Perego20,i, E. Perez Trigo36, A. P´erez-Calero Yzquierdo35, P. Perret5,
G. Pessina20, A. Petrella16,d,37, A. Petrolini19,h, E. Picatoste Olloqui35, B. Pie Valls35,
D. Piedigrossi37, B. Pietrzyk4, D. Pinci22, S. Playfer46, M. Plo Casasus36, M. Poli-Lener18, G. Polok25, A. Poluektov44,33, E. Polycarpo2, D. Popov10, B. Popovici28, S. Poss6,
C. Potterat38, A. Powell51, S. Pozzi16,d, T. du Pree23, V. Pugatch41, A. Puig Navarro35, W. Qian3,7, J.H. Rademacker42, B. Rakotomiaramanana38, I. Raniuk40, G. Raven24, S. Redford51, W. Reece49, A.C. dos Reis1, S. Ricciardi45, J. Riera35,m, K. Rinnert48, D.A. Roa Romero5, P. Robbe7,37, E. Rodrigues47, F. Rodrigues2, C. Rodriguez Cobo36, P. Rodriguez Perez36, G.J. Rogers43, V. Romanovsky34, E. Rondan Sanabria1, M. Rosello35,m, J. Rouvinet38, L. Roy37, T. Ruf37, H. Ruiz35, C. Rummel11, V. Rusinov30, G. Sabatino21,j, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,c, T. Sakhelashvili39, C. Salzmann39, A. Sambade Varela37, M. Sannino19,h, R. Santacesaria22, R. Santinelli37, E. Santovetti21,j, M. Sapunov6, A. Sarti18, C. Satriano22,l, A. Satta21, T. Savidge49, M. Savrie16,d, D. Savrina30, P. Schaack49, M. Schiller11, S. Schleich9, M. Schmelling10, B. Schmidt37, O. Schneider38,
T. Schneider37, A. Schopper37, M.-H. Schune7, R. Schwemmer37, A. Sciubba18,k, M. Seco36,
A. Semennikov30, K. Senderowska26, N. Serra23, J. Serrano6, B. Shao3, M. Shapkin34,
I. Shapoval40,37, P. Shatalov30, Y. Shcheglov29, T. Shears48, L. Shekhtman33, V. Shevchenko30,
A. Shires49, S. Sigurdsson43, E. Simioni24, H.P. Skottowe43, T. Skwarnicki52, N. Smale10,51,
A. Smith37, A.C. Smith37, N.A. Smith48, K. Sobczak5, F.J.P. Soler47, A. Solomin42,
P. Somogy37, F. Soomro49, B. Souza De Paula2, B. Spaan9, A. Sparkes46, E. Spiridenkov29, P. Spradlin51, A. Srednicki27, F. Stagni37, S. Stahl11, S. Steiner39, O. Steinkamp39,
O. Stenyakin34, S. Stoica28, S. Stone52, B. Storaci23, U. Straumann39, N. Styles46, M. Szczekowski27, P. Szczypka38, T. Szumlak47,26, S. T’Jampens4, E. Tarkovskiy30,
E. Teodorescu28, H. Terrier23, F. Teubert37, C. Thomas51,45, E. Thomas37, J. van Tilburg39, V. Tisserand4, M. Tobin39, S. Topp-Joergensen51, M.T. Tran38, S. Traynor12, U. Trunk10, A. Tsaregorodtsev6, N. Tuning23, A. Ukleja27, O. Ullaland37, P. Urquijo52, U. Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16,
J.J. Velthuis42, M. Veltri17,f, K. Vervink37, B. Viaud7, I. Videau7, X. Vilasis-Cardona35,m,
H. Voss10, K. Wacker9, S. Wandernoth11, J. Wang52, D.R. Ward43, A.D. Webber50,
D. Websdale49, M. Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P. Williams44, M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W. Witzeling37, M.L. Woodward45, S.A. Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Yang3, G. Ybeles Smit23, R. Young46, O. Yushchenko34, M. Zeng3, L. Zhang52, Y. Zhang3, A. Zhelezov11, E. Zverev31.
1
Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil
2
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3
Center for High Energy Physics, Tsinghua University, Beijing, China
4
LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5
Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6
CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
7
LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8
LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France
9
Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10
Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11
Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany
12
School of Physics, University College Dublin, Dublin, Ireland
13
Sezione INFN di Bari, Bari, Italy
14
Sezione INFN di Bologna, Bologna, Italy
15
Sezione INFN di Cagliari, Cagliari, Italy
16
Sezione INFN di Ferrara, Ferrara, Italy
17
Sezione INFN di Firenze, Firenze, Italy
18
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19
Sezione INFN di Genova, Genova, Italy
20
Sezione INFN di Milano Bicocca, Milano, Italy
21
Sezione INFN di Roma Tor Vergata, Roma, Italy
22
Sezione INFN di Roma Sapienza, Roma, Italy
23
Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
24
Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, Netherlands
25
Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
26
Faculty of Physics & Applied Computer Science, Cracow, Poland
27
Soltan Institute for Nuclear Studies, Warsaw, Poland
28
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
29
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
32
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
33
Budker Institute of Nuclear Physics (BINP), Novosibirsk, Russia
34
Institute for High Energy Physics (IHEP), Protvino, Russia
35
Universitat de Barcelona, Barcelona, Spain
36
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37
European Organization for Nuclear Research (CERN), Geneva, Switzerland
38
Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland
39
Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
40
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
42
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
43
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44
Department of Physics, University of Warwick, Coventry, United Kingdom
45
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46
47
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
48
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49
Imperial College London, London, United Kingdom
50
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
51
Department of Physics, University of Oxford, Oxford, United Kingdom
52
Syracuse University, Syracuse, NY, United States
53
CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54
Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 aUniversit`a di Bari, Bari, Italy
bUniversit`a di Bologna, Bologna, Italy cUniversit`a di Cagliari, Cagliari, Italy dUniversit`a di Ferrara, Ferrara, Italy eUniversit`a di Firenze, Firenze, Italy fUniversit`a di Urbino, Urbino, Italy
gUniversit`a di Modena e Reggio Emilia, Modena, Italy hUniversit`a di Genova, Genova, Italy
iUniversit`a di Milano Bicocca, Milano, Italy jUniversit`a di Roma Tor Vergata, Roma, Italy kUniversit`a di Roma La Sapienza, Roma, Italy lUniversit`a della Basilicata, Potenza, Italy
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
1
Introduction
Quantum Chromodynamics predicts the cross-section for the production of b-flavoured hadrons in proton-proton collisions, for which higher order calculations are available [1]. The first data taken with the LHCb experiment at 7 TeV centre-of-mass energy allows this cross-section to be measured and compared to predictions. Knowledge of the b yield is also critical in ascertaining the sensitivity of experiments that aim to measure fun-damental parameters of interest involving, for example, CP violation. It is also useful for normalising backgrounds for measurements of higher mass objects that decay into bb, such as the Higgs boson. In this paper we present a measurement of the production cross-section for the average of b-flavoured and b-flavoured hadrons in proton-proton collisions at a centre-of-mass energy of 7 TeV in the pseudorapidity interval 2 < η < 6, where η = −ln [tan(θ/2)], and θ is the angle of the weakly decaying b or b hadron with respect to the proton direction. We extrapolate this measurement to the entire rapidity interval. Our sensitivity extends over the entire range of transverse momentum of the b-flavoured hadron.
The LHCb detector [2] was constructed as a forward spectrometer primarily to measure CP violating and rare decays of hadrons containing b and c quarks. The detector elements are placed along the beam line of the LHC starting with the Vertex Locator (VELO), a silicon strip device that surrounds the proton-proton interaction region and is positioned 8 mm from the beam during collisions. It provides precise locations for primary pp interaction vertices, the locations of decays of long lived hadrons, and contributes to the measurement of track momenta. Other detectors used to measure track momenta comprise a large area silicon strip detector located before a 3.7 Tm dipole magnet, and a combination of silicon strip detectors and straw drift chambers placed afterward. Two Ring Imaging Cherenkov (RICH) detectors are used to identify charged hadrons. Further downstream an Electromagnetic Calorimeter (ECAL) is used for photon detection and electron identification, followed by a Hadron Calorimeter (HCAL), and a system consisting of alternating layers of iron and chambers (MWPC and triple-GEM) that distinguishes muons from hadrons (MUON). The ECAL, MUON, and HCAL provide the capability of first-level hardware triggering.
Two independent data samples, recorded at different times, are examined. For the earliest period of data taking the number of colliding bunches was sufficiently low that the high-level trigger could process all crossings and accept events when at least one track was reconstructed in either the VELO or the tracking stations. This data set, called “microbias”, has an integrated luminosity, L, of 2.9 nb−1. The second sample, referred to
as “triggered”, uses triggers designed to select a single muon. Here L equals 12.2 nb−1.
These samples are analysed independently and the results subsequently combined. Most D0 mesons are produced directly via pp → ccX interactions, where X indicates
any combination of final state particles. These particular D0 mesons are denoted as
“Prompt”. D0 mesons produced in pp → bbX collisions where the b-flavoured hadron
decays into a final state containing a D0 meson are called “Dfb”. We use the decay
advantageous from the point of view of signal to background. Throughout this paper mention of a particular mode implies the inclusion of the charge conjugate mode as well.
2
Analysis of D
0→ K
−π
+The Prompt and Dfb D0 components can be separated statistically by examining the
impact parameter (IP) with respect to the closest primary vertex, where IP is defined as the smallest distance between the D0 reconstructed trajectory and the primary vertex 2.
We use the D0 →K−π+ channel which has a branching fraction of (3.89±0.05)% [4].
The D0 selection criteria are the same regardless of the trigger conditions. Both the
kaon and pion candidates are associated with Cherenkov photons in the RICH system. The photon angles with respect to the track direction are examined and a likelihood formed for each particle hypothesis [2]. Candidates are identified as kaons or pions on the basis of this likelihood. We also require that the momentum transverse to the beam direction, pT, of both the kaon and pion be > 300 MeV, and that their scalar sum is >1400
MeV. (We work in units with c=1.) Since real D0 mesons travel before decaying, the kaon
and pion tracks when followed backwards will most often not point to the closest primary vertex. We require that the χ2 formed by using the hypothesis that the impact parameter
is equal to zero, χ2IP, be > 9 for each track. They also must be consistent with coming from a common origin with vertex fit χ2 < 6. Finally, the D0 candidate must be detached
from the closest primary vertex. To implement this flight distance significance test we form a χ2
FS based on the hypothesis that the flight distance between the primary and D0
vertices is zero, and require χ2
FS > 64. This set of requirements on the D0 candidate is
labeled “generic”. All of these requirements were selected by comparing sidebands of the invariant K−π+ mass distribution, representative of the background, with signal Monte
Carlo simulation using PYTHIA 6.4 [5].
In order to ascertain the parameters characterizing the D0 mass peak, a sample
en-riched in Prompt D0 mesons is selected. This is achieved by including two additional
requirements: (1) the cosine of the angle between the D0 candidate’s momentum
di-rection and the line from the K−π+ vertex to the primary vertex must be > 0.9999,
and (2) the χ2
IP for the D0 must be less than 25. The K−π+ invariant mass
distribu-tion after imposing all of these requirements is shown in Fig. 1. The data are fit with a double-Gaussian signal function, with both Gaussians having the same mean, and a linear background. This signal shape is used in all subsequent fits.
Selecting K−π+ candidates within ±20 MeV of the fitted D0 mass peak and
subtract-ing the background ussubtract-ing invariant mass sidebands 35-75 MeV from the peak on both sides, we display the distribution of the natural logarithm of the D0 candidate’s IP in
Fig. 2. Both Prompt and Dfb components are visible. The IP for the Prompt signal would be zero without the effects of resolution. The Prompt shape is described by a
bi-2
Primary vertices are found using an iterative procedure based on the closest approach of tracks with each other. The resolutions of the resulting vertex positions depend on the number of tracks and are of the order of 70 µm along the beam direction and 10 µm in each transverse coordinate, for 40 tracks.
LHCb Events / (2 MeV) 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 ) (MeV + π -m(K 1800 1850 1900 1950 ) 1800 1850 1900 1950
Figure 1: K−π+ invariant mass for “Prompt” selection criteria in 2.9 nb−1. The curve shows
a fit to a linear background (dashed) plus double-Gaussian signal function with parameters σ1=7.1±0.6 MeV, σ2/σ1=1.7±0.1, and the fraction of the second Gaussian 0.40±0.16.
-6 -4 -2 0 2 ln(IP/mm) 0 200 400 600 800 1000 Events/ (0.1) LHCb
Figure 2: Natural logarithm of the IP for D0 mesons, with the IP in units of mm (points with error bars) for the 2.9 nb−1 microbias sample. Background has been subtracted using mass
sidebands. The dashed curve shows the result of the fit to the Prompt component, the dotted line the Dfb component, and the histogram the sum of the two.
furcated double-Gaussian function. The distribution for Dfb is widely spread as the finite b lifetime causes the D0 meson not to point to the primary vertex; we use a Monte-Carlo
simulated shape. The histogram in Fig. 2 shows the results of a fit to the two components, letting the parameters of the Prompt shape float; this shape is used in systematic studies.
3
Evaluation of the b → D
0Xµ
−ν yields
3.1
Using microbias data
To select the decay chain b → D0Xµ−ν, D0 →K−π+ and enrich our b sample, we match
D0 candidates with tracks identified as muons, by ensuring that they penetrate the iron
of the MUON system and have minimum ionization in the calorimeters [2]. Right-sign (RS) combinations have the sign of the charge of the muon being the same as the charge of the kaon in the D0 decay. Wrong-sign (WS) combinations have the signs of the charges
of the kaon and the muon being opposite; they are highly suppressed in semileptonic b decay. WS events are useful to estimate certain backgrounds.
To find b candidates we select D0 candidates using the generic criteria specified above,
and add a track that is identified as a muon, has pT > 500 MeV, and has χ2IP > 4.
The D0 and muon candidates are required to form a common vertex with χ2 < 5, the
D0µ− invariant mass must be between 3 and 5 GeV, and the cosine of the angle of the b
pseudo-direction, formed from the D0 and muon vector momentum sum with respect to
the line between the D0µ− vertex and the primary vertex, must be > 0.998. This angle
cut is loose enough to have about 97% efficiency for b → D0Xµ−ν decays when taking
into account the effect of the missing neutrino momentum. We measure η using the line defined by connecting the primary event vertex and the vertex formed by the D0 and the
µ−. Bins in η are chosen to be larger than the resolution to obviate the need for any
cross-feed corrections. Events are accepted in the interval 2 < η < 6.
The IP distributions of both RS and WS candidates, requiring that the K−π+
invari-ant mass is within 20 MeV of the D0 mass, are shown in Fig. 3. We perform an unbinned
extended maximum likelihood fit to the two-dimensional distributions in K−π+ invariant
mass over a region extending ±100 MeV from the D0 mass peak, and ln(IP/mm). This
fitting procedure allows us directly to determine the background shape from false combi-nations under the D0 signal mass peak. The parameters of the Prompt IP distribution
are found by applying the same criteria as for Fig. 3, but with the additional track failing the muon identification criteria. The Monte Carlo simulated shape is used for the Dfb component.
The fit yields in the RS sample are 84.1±10.4 Dfb events, 16.3±5.4 Prompt events, and 14.0±1.9 background. In the WS the corresponding numbers are 0.0±1.1 Dfb events, 14.9±4.2 Prompt events, and 10.1±1.5 background. The Prompt yields are consistent between RS and WS as expected.
The contribution of tracks misidentified as muons (fakes) in both the RS and WS sam-ples is evaluated by counting the number of tracks that satisfy all our criteria by forming a common vertex with a D0 signal candidate, but do not satisfy our muon identification
criteria. These tracks are categorized by their identity as electrons using ECAL, or pions, kaons or protons using the RICH. These samples are then multiplied by the relevant fake rates that were estimated from simulation and checked with data. The resulting ln(IP) distributions are examined, resulting in estimates of 2.2±0.4 RS Dfb fakes and 1.1±0.4 WS Dfb fakes. The B(b → D0Xτ−ν, τ− →µ−νν) of (0.36±0.11)% is (5.3±1.6)% of the
ln(IP/mm) 6 4 2 0 2 Events / (0.5) 0 5 10 15 20 25 30 0 2 0 5 10 15 20 25 30 (a) LHCb ln(IP/mm) 6 4 2 0 2 Events / (0.5) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 (b) LHCb
Figure 3: Natural logarithm of the D0 IP in the 2.9 nb−1 microbias sample for (a) right-sign
and (b) wrong-sign D0-muon candidate combinations. The dotted curves show the D0 sideband backgrounds, the thin solid curves the Prompt yields, the dashed curve the Dfb signal, and the thick solid curves the totals.
semimuonic decay [3]. However, the relative efficiency to detect the resulting secondary muon is only 29% leading to a 1.5% subtraction. The lower efficiency is due to the lower secondary muon momentum from τ decay and the finite τ lifetime that causes some events to fail the vertex χ2 requirement. Other sources of backgrounds from b-hadron decays
as evaluated by Monte Carlo simulation are small within our selection requirements, and predicted to be similar in size to the WS yields that are consistent with zero.
3.2
Using muon triggered data
The trigger imposes a cut of pT > 1.3 GeV on muon candidates. The IP distributions
for both RS and WS combinations are shown in Fig. 4. We find a total of 195.4±14.9 RS Dfb, and 8.8±5.1 WS Dfb events. The Prompt contributions are determined to be 9.3±4.8 RS with 5.3±3.0 WS.
In order to extract the b cross-section from this data sample we have to make an additional correction for the overall η-dependent trigger efficiency. The Monte Carlo simulated efficiency is checked using data by studying J/ψ → µ+µ− decays in microbias
events or those that triggered independently of the single muon trigger. The data show a somewhat larger relative efficiency than the simulation, from 2% at low η rising to 11% at high η. We correct for this factor and use the 2% error determined on the correction, to account for its uncertainty, that we add to the statistical error of this sample.
The IP distributions in each η bin in both trigger samples are fit independently to the same functions as described above to extract the η-dependent event yields. The yields are listed in Table 1. Muon fakes and the τ− contribution are subtracted in the same
manner as in the microbias sample. In the triggered sample the hadron-to-muon fake rates are smaller as a result of the harder muon pT cut imposed by the trigger of 1300 MeV
rather than the 500 MeV used in analysing the microbias sample. The RS Dfb fakes total 1.0±0.2 and the WS Dfb fakes total 0.6±0.2 events. A uniform 1.5% τ− subtraction is
ln(IP/mm) -6 -4 -2 0 2 Events / (0.5) 0 10 20 30 40 50 0 2 0 10 20 30 40 50 ln(IP/mm) 0 2 Events / (0.5) 0 2 -6 -4 -2 LHCb (a) LHCb (b) 0 10 20 30 40 50 0 10 20 30 40 50
Figure 4: Natural logarithm of the D0 IP in the 12.2 nb−1 triggered sample for (a) right-sign
and (b) wrong-sign D0-muon candidate combinations. The dotted curves show the D0 sideband
backgrounds, the thin solid curves the Prompt yields, the dashed curve the Dfb signal, and the thick solid curves the totals.
done in each η bin.
Table 1: RS background subtracted event yields from data, and extracted cross-sections, com-pared with predictions from MCFM [7] and FONLL [8]. The systematic uncertainties in the normalisation of 17.3% are not included. The uncertainties on the FONLL prediction are+45
−38%,
while those for MCFM are +83
−44%.
Bin Event yields σ(pp → HbX) (µb)
Microbias Trig. Microbias Trig. Average MCFM FONLL
2 < η < 3 16.7±4.5 48.8±7.5 27.2±7.3 29.7±4.6 29.0±3.9 37.8 28.9 3 < η < 4 50.1±8.0 111.4±11.0 28.8±4.6 28.8±2.8 28.8±2.4 27.1 22.4 4 < η < 5 18.1±5.0 30.2±6.0 13.3±3.7 11.7±2.3 12.2±2.0 16.7 13.1 5 < η < 6 4.7±2.8 5.2±2.2 6.5±3.6 4.8±2.5 5.3±2.0 7.4 5.9 Sum 89.6±10.8 195.6±14.9 75.9±10.0 75.0±6.5 75.3±5.4 89.0 70.2
4
Luminosity determination and systematic
uncer-tainties
The luminosity was measured at specific periods during the data taking using both Van der Meer scans and the ‘beam-profile’ method [6]. Two Van der Meer scans were performed in a single fill. Analysis of these scans yielded consistent results for the absolute luminosity scale with a precision of around 10%, dominated by the uncertainty in the knowledge of the beam currents. In the second approach, six separate periods of stable running were chosen, and the beam-profiles measured using beam-gas and beam-beam interactions.
Using these results, correcting for crossing angle effects, and knowing the beam currents, we determine the luminosity in each period following the analysis procedure described in Ref. [6]. Consistent results were found for the absolute luminosity scale in each period, with a precision of 10%, again dominated by the beam current uncertainty. These results are in good agreement with those of the Van der Meer analysis.
The knowledge of the absolute luminosity scale was used to calibrate the number of VELO tracks reconstructed using only the R sensors [2], which are found to have a stable response throughout the data-taking period. The integrated luminosities of the runs considered in this analysis were determined to be (2.85±0.29) and (12.2±1.2) nb−1,
respectively, for the microbias and triggered samples.
The product of detector acceptance, tracking efficiencies and our analysis cuts, as estimated by Monte Carlo simulation, is about 8% for b hadrons produced in the region 2 < η < 6. The systematic uncertainty on the tracking efficiency is evaluated by comparing the ratio of D0 → K−π+π+π− to D0 → K−π+ events in data to the ratio in simulation.
We find that the ratio of data to Monte Carlo efficiencies is 1.00±0.03 for tracks from D0
decay, and use 3% as the uncertainty per track. For the higher momentum muon track 4% is used. The total tracking uncertainty then being fully correlated is taken as 10%, where this uncertainty is dominated by the size of the data sample. The kaon and pion RICH identification efficiencies are determined in each η bin from a comparison of D0 →K−π+
yields evaluated both with and without kaon identification. An error of 1.5% is set on the particle identification efficiencies that is mostly due to the kaon, as the pion selection criteria are much looser.
The efficiency of our muon selection criteria with respect to that obtained from the Monte Carlo simulation is evaluated as a function of momentum by detecting J/ψ → µ+µ−
decays where one muon is identified by passing our muon identification criteria while the opposite-sign track must have been biased neither by the muon trigger, nor the muon identification criteria. Using the momentum weighted averages we find (data/MC) = (96.9+2.4−2.5)%. We correct for the difference and assign a 2.5% error to our muon identifica-tion.
Since the b → D0Xµ−ν detection efficiency changes linearly with p
Tby about a factor
of four from zero to 12 GeV and then stays flat, the efficiency will not be estimated cor-rectly if the Monte Carlo generator does not accurately simulate the pT distribution. We
investigate this possible efficiency change by examining the difference between the mea-sured and simulated summed pT distribution of the D0 plus muon. They are consistent,
and an uncertainty of 3% is assigned as the systematic error from considerations of how large a difference the data allow.
Because the detection efficiency is different for D0 mesons that result from B− →
D(∗)0µ−ν compared to those from other b decays (such as B0 →D∗+µ−ν, B → D∗∗µ−ν,
B0s →D∗∗
s µ−ν, or similarly from Λb), we include an uncertainty due to the precision of our
knowledge of the branching fractions [4]. By varying these rates within their errors, we find an uncertainty of 4.4%. As discussed below, to translate our results on the yields into cross-section measurements we assume the fractions for fragmentation into the different b-hadron species as measured by LEP. Varying these values within their errors gives a
Table 2: Systematic uncertainties.
Source Error (%) Source Error (%)
Luminosity 10.0 Prompt & Dfb shapes 1.4
Tracking efficiency 10.0 B(D0 →K−π+) 1.3
B(b → D0Xµ−ν) 5.1 D0µ− vertex χ2 cut 1.2
Assumed branching fractions 4.4 Kaon identification 1.2
LEP fragmentation fractions 4.2 Muon fakes 1.0
Generated b pT distribution 3.0 D0 mass cut 1.0
Muon identification 2.5 D0 vertex χ2 cut 0.6
χ2
IP cut 2.5 D0 flight distance cut 0.4
MC statistics 1.5 Pion identification 0.3
Total 17.3%
systematic uncertainty of 4.2%.
The efficiency of the various selection criteria with respect to simulation has been evaluated by changing the cuts. The resulting changes of the yield are small. The D0µ−
vertex χ2 cut efficiency was cross-checked comparing data and Monte Carlo using Ξ− → Λπ−decays. All of the uncertainties considered are listed in Table 2. The total systematic
uncertainty due to all sources added in quadrature is 17.3%.
5
Cross-sections and comparison with theory
The extracted cross-sections are listed in Table 1. The η-dependent cross-section is shown in Fig. 5 for both data sets and the average. The agreement between the two data sets is excellent.
We compare with two theories that predict b production cross-sections as a function of η. MCFM [7] predicts the cross-section for bb quark production in next to leading order (NLO) using the MSTW8NL parton distribution function (PDF). The FONLL [8] prediction uses the CTEQ6.5 PDF, and improves the NLO result with the resummation of pT logarithms up to next-to-leading order. It also includes the b-quark fragmentation
into hadrons. The measured yields are averaged over b-flavoured and b-flavoured hadrons, Hb, in η intervals:
σ(pp → HbX) =
# of detected D0µ− and D0µ+ events
2L × efficiency × B(b → D0Xµ−ν)B (D0 →K−π+). (1)
Averaging the cross-sections from both samples, and summing over η, we measure
σ(pp → HbX) = (75.3 ± 5.4 ± 13.0) µb (2)
in the interval 2 < η < 6. The first error is statistical, the second systematic. The LEP fragmentation fractions are used for our central values [9]. Use of these fractions
Figure 5: σ(pp → HbX) as a function of η for the microbias (×) and triggered (•) samples,
shown displaced from the bin center and the average (+). The data are shown as points with error bars, the MCFM prediction as a dashed line, and the FONLL prediction as a thick solid line. The thin upper and lower lines indicate the theoretical uncertainties on the FONLL prediction. The systematic uncertainties in the data are not included.
provides internal consistency to our results as B(b → D0Xµ−ν) was also measured at
LEP. The measured value changes if the b-hadron fractions differ. Fractions have also been measured at the Tevatron, albeit with large uncertainties [9]. The largest change with respect to LEP is that the b-baryon percentage rises from (9.1±1.5)% to (21.4±6.8)%. If the Tevatron fractions are used, our result changes to (89.6±6.4±15.5) µb.
6
Conclusions
The cross-section to produce b-flavoured hadrons is measured to be
σ(pp → HbX) = (75.3 ± 5.4 ± 13.0) µb (3)
in the pseudorapidity interval 2 < η < 6 over the entire range of pT assuming the LEP
fractions for fragmentation into b-flavoured hadrons. For extrapolation to the full η region, theories predict factors of 3.73 (MCFM), and 3.61 (FONLL), while PYTHIA 6.4 gives 3.77. Using a factor of 3.77 for our extrapolation, we find a total bb cross-section of
σ(pp → bbX) = (284 ± 20 ± 49) µb (4)
based on the LEP fragmentation results; using the Tevatron fragmentation fractions the result increases by 19%. The quoted systematic uncertainty does not include any contri-bution relating to the extrapolation over the η range where LHCb has no sensitivity.
The production of b-flavoured hadrons has been measured in pp collisions in 1.8 and 1.96 TeV collisions at the Tevatron. The earlier measurements at 1.8 TeV appeared to be
higher than the NLO theoretical predictions [10]. More recent measurements by the CDF collaboration at 1.96 TeV are consistent with the NLO theory [11]. The history has been reviewed by Mangano [12]. Here, with a large energy increase to 7 TeV, we find that the measured cross-section is consistent with theoretical predictions, both in normalization and η-dependent shape.
Acknowledgments
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at CERN and at the LHCb institutes, and acknowledge support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN, XUNGAL and GENCAT (Spain); SNSF and SER (Switzer-land); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowl-edge the support received from the ERC under FP7 and the R´egion Auvergne.
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